The Development of a Space Climatology: 2. The Distribution of Power Input Into the Magnetosphere on a 3-Hourly Timescale

Paper 1 in this series (Lockwood et al., 2018a, https://doi.org/10.1029/2018SW001856) showed that the power input into the magnetosphere Pα is an ideal coupling function for predicting geomagnetic “range” indices that are strongly dependent on the substorm current wedge and that the optimum coupling exponent α is 0.44 for all averaging timescales, τ, between 1 min and 1 year. The present paper explores the implications of these results. It is shown that the form of the distribution of Pα at all averaging timescales τ is set by the interplanetary magnetic field orientation factor via the nature of solar wind-magnetosphere coupling (due to magnetic reconnection in the dayside magnetopause) and that at τ = 3 hr (the timescale of geomagnetic range indices) the normalized Pα (divided by its annual mean, that is, τ=3hr/τ=1yr) follows a Weibull distribution with k of 1.0625 and λ of 1.0240. This applies to all years to a useful degree of accuracy. It is shown that exploiting the constancy of this distribution and using annual means to predict the full distribution gives the probability of space weather events in the largest 10% and 5% to within uncertainties of magnitude 10% and 12%, respectively, at the one sigma level.